Lagrangian multi-particle statistics

Lüthi, Beat; Berg, Jacob; Ott, Søren; Mann, Jakob

doi:10.1007/978-1-4020-6218-6_21

Cited by 18 publications

(25 citation statements)

References 27 publications

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“…The orthogonality betweenẽ ω and e 3 also decreases with increasing scale. These results are consistent with previous data (Luthi et al 2007;Pumir et al 2013;Danish & Meneveau 2018) whereÃ was computed using different coarse-graining methods. In figure 5(b), we see that vorticity reaches a peak alignment with e R1 after a time delay of t ≈ 3τ N , almost independent of the scale l/η (Xu et al 2011;Pumir et al 2013).…”

Section: Vorticity Alignmentsupporting

confidence: 93%

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

2018

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We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.

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Section: Vorticity Alignmentsupporting

confidence: 93%

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

2018

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“…6 and 7 is that it is not possible to either identify a clear Richardson scaling or distinguish between Richardson and Batchelor scaling from these figures. This limitation is quite common to numerical studies based on direct numerical simulation 16,55 but was also encountered in experiments, 56,57 and arises because the flow Reynolds number is not large enough to provide the separation of scales that is required to observe a wide enough inertial range. It is thus believed that a broad crossover from the dissipation regime (in which separation grows exponentially) to the diffusion regime exists that hides the intermediate inertial range regime.…”

Section: (T)mentioning

confidence: 99%

Anisotropy in pair dispersion of inertial particles in turbulent channel flow

et al. 2012

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The rate at which two particles separate in turbulent flows is of central importance to predict the inhomogeneities of particle spatial distribution and to characterize mixing. Pair separation is analyzed for the specific case of small, inertial particles in turbulent channel flow to examine the role of mean shear and small-scale turbulent velocity fluctuations. To this aim an Eulerian-Lagrangian approach based on pseudo-spectral direct numerical simulation (DNS) of fully developed gas-solid flow at shear Reynolds number Re τ = 150 is used. Pair separation statistics have been computed for particles with different inertia (and for inertialess tracers) released from different regions of the channel. Results confirm that shear-induced effects predominate when the pair separation distance becomes comparable to the largest scale of the flow. Results also reveal the fundamental role played by particles-turbulence interaction at the small scales in triggering separation during the initial stages of pair dispersion. These findings are discussed examining Lagrangian observables, including the mean square separation, which provide prima facie evidence that pair dispersion in non-homogeneous anisotropic turbulence has a superdiffusive nature and may generate non-Gaussian number density distributions of both particles and tracers. These features appear to persist even when the effects of shear dispersion are filtered out, and exhibit strong dependency on particle inertia. Application of present results is discussed in the context of modelling approaches for particle dispersion in wall-bounded turbulent flows. C 2012 American Institute of Physics. [http://dx

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“…The velocity gradients constitute a convenient descriptor of the fundamental structure of turbulent flows and some of their statistics reflect the out-of-equilibrium nature of turbulence. Although the velocity gradients describe only the structure of the small scales, the statistical distributions of the filtered velocity gradients are invariant across scales and reveal the self-similar structure of the inertial range [30,80,107,108]. Some investigations suggest a connection between the velocity gradients in the inertial scales and the energy cascade [30,40,109], and common SGS models rely on the assumption that energy transfer towards the unresolved scales can be reproduced using the velocity gradients of the resolved scales [85,97,110].…”

Section: Direct Cascadesmentioning

confidence: 99%

Entropy, chaos and irreversibility in the turbulence energy cascade

Martín¹

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This thesis studies the turbulent energy cascade from the perspective of statistical mechanics and relates inter-scale energy fluxes to information-entropy production. The microscopical reversibility of the energy cascade is tested by constructing a reversible 3D turbulent system using a dynamic model for the sub-grid stresses. This system, when reversed in time, develops a sustained inverse cascade towards the large scales, evidencing that the characterization of the inertial energy cascade must consider the possibility of an inverse regime. This experiment suggests the introduction of a probabilistic concept, namely entropy, to explain the prevalence of direct over inverse energy cascades. Entropy production, as a statistical property of ensembles in phase space, is connected to the dynamics of the energy cascade in physical space by considering the space locality of the energy fluxes and their relation to the local structure of the flow. An entropic mechanism for the prevalence of direct energy transfer is proposed based on the dynamics of the rate-of-strain tensor, which is identified as an important indicator of statistical irreversibility in the energy cascade. A deeper analysis of the entropy generation mechanisms is accomplished by defining a space-local measure of phase-space mixing based on the Lyapunov exponents. The statistics of this quantity consistently reveal that the dynamics of the rate-of-strain tensor are fundamentally connected to entropy production. This analysis, which also describes the spatio-temporal structure of chaos in the energy cascade, reveals a strong localization of highly chaotic and entropy-producing events in the vicinity of interacting vortical structures. I would like to thank my family, specially Nadia, friends, and work colleagues for their support and encouragement during the final stages of this thesis. I thank Lindy Hop for making these years probably one of the happiest times in my life, and for not letting me take anything too seriously. I would like to thank my advisor, Javier Jiménez, for choosing a beautiful topic that has allowed me to get in touch with the fascinating field of non-equilibrium thermodynamics. I also thank him for passive and actively fostering my independence.

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Lagrangian multi-particle statistics

Cited by 18 publications

References 27 publications

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

Anisotropy in pair dispersion of inertial particles in turbulent channel flow

Entropy, chaos and irreversibility in the turbulence energy cascade

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